There are presently a wide variety of masks that are designed for use by sport divers. In their present form, many such diving masks are closely analogous to "blinders" on a horse, narrowing the horizontal field of view and similarly restricting the vertical field of view. Additionally, the refractive properties of the ambient water further narrow the diver's field of view through the front port of the mask. As a result, many things of interest to the diver go unobserved. In particular, conventional masks do not allow a diver to easily see the straps or controls of his buoyancy compensator, let alone his weight belt or anything attached to it. This limitation is more than an inconvenience. If the diver becomes entangled in heavy monofilament fishing line, kelp, etc., the lack of easy self-inspection can be dangerous, particularly for an inexperienced diver.
Some masks have a greater field of view than others, but, as shown by the experiments of Weldman et al. ("Visual Fields of the Scuba Diver," Weldman, G., Christianson, R. A., and Egstrom, G. H., Human Factors 7, 423-430, 1965), few have a total horizontal field of view greater than about 80.degree.. In order to mitigate this restriction, masks with side glass panels were introduced that provide approximately an additional 25.degree. of view directly to the sides of the diver. Also, as is described below in greater detail, when side panels are used, gaps of about 25.degree. are present between the diver's field of vision through the front and side ports.
A common element of virtually all diving masks is a flat front port of a transparent material, which is commonly a tempered glass plate. The glass and water both have indices of refraction greater than that of air, and this is a major source of the restriction in the diver's field of vision. Although the glass port is necessary to provide an air interface with the diver's eyes, the glass itself plays a minor role in determining the underwater field of vision.
FIG. 1a illustrates the refraction of a light ray passing from water through a flat glass port into air. Under Snell's Law: EQU n.sub.air sin .THETA..sub.air =n.sub.glass sin .THETA..sub.1 glass EQU n.sub.glass sin .THETA..sub.2 glass =n.sub.water sin .THETA..sub.water
where n.sub.air n.sub.water and n.sub.glass are the indices of refraction of air, water and glass, respectively, and .THETA..sub.air, .THETA..sub.water and .THETA..sub.glass, are the angles of the light ray off of the respective boundary normals within air, water and glass, respectively.
Because the surfaces of the port are both flat and parallel, the internal angles of the light ray at both surfaces of the glass port are the same (.THETA..sub.1 glass =.THETA..sub.2 glass .ident..THETA..sub.glass) and thus, other than creating a minor displacement (less than the thickness of the port), the port plays no role in determining the optical path. Accordingly, the equations combine: EQU n.sub.air sin .THETA..sub.air =n.sub.water sin .THETA..sub.water
with the angle in water independent of the index of refraction of the glass port.
Thus, the viewing angle in water may be calculated as a function of the initial angle in air without regard to the particular transparent material used for the port (n.sub.air =1.00 and, for sea water at 20.degree. C., n.sub.water =1.34). The results of these calculations are presented in Table 1:
TABLE 1 ______________________________________ .THETA..sub.air (deg) .THETA..sub.water (deg) ______________________________________ 0 0 10 7.5 20 14.8 30 21.9 40 28.7 50 34.9 60 40.3 70 44.5 80 47.3 90 48.3 ______________________________________
It can thus be seen that no matter how close the port is to the eyes or how extensive the port is, the line of sight in water has a fundamental limitation to less than 49.degree.. The resultant total lateral field of view in water is less than 97.degree..
When light rays pass through a prism or simply curved lens, the two faces of glass are not parallel but are at an angle to each other, and the calculations are slightly altered. As shown in FIG. 1b, two surfaces through which a light ray passes are separated by an angle .THETA..sub.P, shown as the included angle of a triangular-section prism. As is known from Snell's Law: EQU n.sub.air sin .THETA..sub.air =n.sub.glass sin .THETA..sub.1 glass EQU n.sub.glass sin .THETA..sub.2 glass =n.sub.water sin .THETA..sub.water
Furthermore, geometrically: EQU .THETA..sub.2 glass =.THETA..sub.1 glass +.THETA..sub.P
It can accordingly be seen that, given .THETA..sub.P, n.sub.glass and .THETA..sub.air, the equations may be solved for .THETA..sub.water. Similarly, for a given deflection of the view line (.THETA..sub.water -.THETA..sub.air -.THETA..sub.P), the equations may be solved to determine .THETA..sub.P and n.sub.glass or vice versa.
By example, if .THETA..sub.air =0, then .THETA..sub.1 glass =0 and: EQU .THETA..sub.2 glass =.THETA..sub.P EQU n.sub.water sin .THETA..sub.water =n.sub.glass sin .THETA..sub.P
Solving for .THETA..sub.water : EQU .THETA..sub.water =sin.sup.-1 ((n.sub.glass /n.sub.water) sin .THETA..sub.P
Similarly, solving for .THETA..sub.P : EQU .THETA..sub.P =sin.sup.-1 ((n.sub.water /n.sub.glass) sin .THETA..sub.water)
If geometry constraints dictate .THETA..sub.P, the equation can be solved for the necessary index of refraction to achieve a certain .THETA..sub.water : EQU n.sub.glass =n.sub.water (sin .THETA..sub.water /sin .THETA..sub.P)
Vertical Line of Sight and Self-Inspection
As shown schematically in FIG. 2, for a typical mask, the maximum downward internal viewing angle .THETA..sub.air (from the eyes of the wearer to the base of the front port) is approximately 55.degree.. The corresponding maximum downward viewing angle in water .THETA..sub.water is therefore 37.7.degree., an angle that precludes a direct view of the diver's upper body or any equipment attached to it.